Count number of triplets with product equal to given number

Given an array of distinct integers(considering only positive numbers) and a number ‘m’, find the number of triplets with product equal to ‘m’.

Examples: 

Input : arr[] = { 1, 4, 6, 2, 3, 8}  
            m = 24
Output : 3
{1, 4, 6} {1, 3, 8} {4, 2, 3}

Input : arr[] = { 0, 4, 6, 2, 3, 8}  
            m = 18
Output : 0

Asked in : Microsoft

A Naive approach is to consider each and every triplet one by one and count if their product is equal to m.  

Implementation:

C++

// C++ program to count triplets with given
// product m
#include <iostream>
using namespace std;

// Function to count such triplets
int countTriplets(int arr[], int n, int m)
{
    int count = 0;

    // Consider all triplets and count if
    // their product is equal to m
    for (int i = 0; i < n - 2; i++)
        for (int j = i + 1; j < n - 1; j++)
            for (int k = j + 1; k < n; k++)
                if (arr[i] * arr[j] * arr[k] == m)
                    count++;

    return count;
}

// Drivers code
int main()
{
    int arr[] = { 1, 4, 6, 2, 3, 8 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int m = 24;

    cout << countTriplets(arr, n, m);

    return 0;
}

Java

// Java program to count triplets with given
// product m

class GFG {
    // Method to count such triplets
    static int countTriplets(int arr[], int n, int m)
    {
        int count = 0;

        // Consider all triplets and count if
        // their product is equal to m
        for (int i = 0; i < n - 2; i++)
            for (int j = i + 1; j < n - 1; j++)
                for (int k = j + 1; k < n; k++)
                    if (arr[i] * arr[j] * arr[k] == m)
                        count++;

        return count;
    }

    // Driver method
    public static void main(String[] args)
    {
        int arr[] = { 1, 4, 6, 2, 3, 8 };
        int m = 24;

        System.out.println(countTriplets(arr, arr.length, m));
    }
}

Python3

# Python3 program to count
# triplets with given product m

# Method to count such triplets
def countTriplets(arr, n, m):

    count = 0

    # Consider all triplets and count if
    # their product is equal to m
    for i in range (n - 2):
        for j in range (i + 1, n - 1):
            for k in range (j + 1, n):
                if (arr[i] * arr[j] * arr[k] == m):
                    count += 1
    return count

# Driver code
if __name__ == "__main__":

    arr = [1, 4, 6, 2, 3, 8]
    m = 24
    print(countTriplets(arr,
                        len(arr), m))

# This code is contributed by Chitranayal

C#

// C# program to count triplets
// with given product m
using System;

public class GFG {

    // Method to count such triplets
    static int countTriplets(int[] arr, int n, int m)
    {
        int count = 0;

        // Consider all triplets and count if
        // their product is equal to m
        for (int i = 0; i < n - 2; i++)
            for (int j = i + 1; j < n - 1; j++)
                for (int k = j + 1; k < n; k++)
                    if (arr[i] * arr[j] * arr[k] == m)
                        count++;

        return count;
    }

    // Driver method
    public static void Main()
    {
        int[] arr = { 1, 4, 6, 2, 3, 8 };
        int m = 24;

        Console.WriteLine(countTriplets(arr, arr.Length, m));
    }
}

// This code is contributed by Sam007

PHP

<?php
// PHP program to count triplets
// with given product m

// Function to count such triplets
function countTriplets($arr, $n, $m)
{
    $count = 0;

    // Consider all triplets and count if
    // their product is equal to m
    for ( $i = 0; $i < $n - 2; $i++)
        for ( $j = $i + 1; $j < $n - 1; $j++)
            for ($k = $j + 1; $k < $n; $k++)
                if ($arr[$i] * $arr[$j] * $arr[$k] == $m)
                    $count++;

    return $count;
}

    // Driver code
    $arr = array(1, 4, 6, 2, 3, 8);
    $n = sizeof($arr);
    $m = 24;
    echo countTriplets($arr, $n, $m);

// This code is contributed by jit_t.
?>

Javascript

<script>
// Javascript program to count triplets with given
// product m

    // Method to count such triplets
    function countTriplets(arr,n,m)
    {
        let count = 0;

        // Consider all triplets and count if
        // their product is equal to m
        for (let i = 0; i < n - 2; i++)
            for (let j = i + 1; j < n - 1; j++)
                for (let k = j + 1; k < n; k++)
                    if (arr[i] * arr[j] * arr[k] == m)
                        count++;

        return count;
    }

    // Driver method
    let arr = [ 1, 4, 6, 2, 3, 8];
    let m = 24;
    document.write(countTriplets(arr, arr.length, m));

    // This code is contributed by avanitrachhadiya2155

</script>

Output

3

Time Complexity: O(n³)
Auxiliary Space: O(1)

An Efficient Method is to use Hashing.  

1. Store all the elements in a hash_map with their index.
2. Consider all pairs(i, j) and check the following: 
   • If (arr[i]*arr[j] !=0 && (m % arr[i]*arr[j]) == 0), If yes, then search for ( m / (arr[i]*arr[j]) in the map.
   • Also check m / (arr[i]*arr[j]) is not equal to arr[i] and arr[j].
   • Also, check that the current triplet is not counted previously by using the index stored in the map.
   • If all the above conditions are satisfied, then increment the count.
3. Return count.

Implementation:

C++

// C++ program to count triplets with given
// product m
#include <bits/stdc++.h>
using namespace std;

// Function to count such triplets
int countTriplets(int arr[], int n, int m)
{
    // Store all the elements in a set
    unordered_map<int, int> occ;
    for (int i = 0; i < n; i++)
        occ[arr[i]] = i;

    int count = 0;

    // Consider all pairs and check for a
    // third number so their product is equal to m
    for (int i = 0; i < n - 1; i++) {
        for (int j = i + 1; j < n; j++) {
            // Check if current pair divides m or not
            // If yes, then search for (m / arr[i]*arr[j])
            if ((arr[i] * arr[j] <= m) && (arr[i] * arr[j] != 0) && (m % (arr[i] * arr[j]) == 0)) {
                int check = m / (arr[i] * arr[j]);
                auto it = occ.find(check);

                // Check if the third number is present
                // in the map and it is not equal to any
                // other two elements and also check if
                // this triplet is not counted already
                // using their indexes
                if (check != arr[i] && check != arr[j]
                    && it != occ.end() && it->second > i
                    && it->second > j)
                    count++;
            }
        }
    }

    // Return number of triplets
    return count;
}

// Drivers code
int main()
{
    int arr[] = { 1, 4, 6, 2, 3, 8 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int m = 24;

    cout << countTriplets(arr, n, m);

    return 0;
}

Java

// Java program to count triplets with given
// product m

import java.util.HashMap;

class GFG {
    // Method to count such triplets
    static int countTriplets(int arr[], int n, int m)
    {
        // Store all the elements in a set
        HashMap<Integer, Integer> occ = new HashMap<Integer, Integer>(n);
        for (int i = 0; i < n; i++)
            occ.put(arr[i], i);

        int count = 0;

        // Consider all pairs and check for a
        // third number so their product is equal to m
        for (int i = 0; i < n - 1; i++) {
            for (int j = i + 1; j < n; j++) {
                // Check if current pair divides m or not
                // If yes, then search for (m / arr[i]*arr[j])
                if ((arr[i] * arr[j] <= m) && (arr[i] * arr[j] != 0) && (m % (arr[i] * arr[j]) == 0)) {
                    int check = m / (arr[i] * arr[j]);

                    occ.containsKey(check);

                    // Check if the third number is present
                    // in the map and it is not equal to any
                    // other two elements and also check if
                    // this triplet is not counted already
                    // using their indexes
                    if (check != arr[i] && check != arr[j]
                        && occ.containsKey(check) && occ.get(check) > i
                        && occ.get(check) > j)
                        count++;
                }
            }
        }

        // Return number of triplets
        return count;
    }

    // Driver method
    public static void main(String[] args)
    {
        int arr[] = { 1, 4, 6, 2, 3, 8 };
        int m = 24;

        System.out.println(countTriplets(arr, arr.length, m));
    }
}

Python3

# Python3 program for the above approach

# Function to find the triplet
def countTriplets(li,product):
    flag = 0
    count = 0

    # Consider all pairs and check
    # for a third number so their
    # product is equal to product
    for i in range(len(li)):

        # Check if current pair
        # divides product or not
        # If yes, then search for
        # (product / li[i]*li[j])
        if li[i]!= 0 and product % li[i] == 0:

            for j in range(i+1, len(li)):

                # Check if the third number is present
                # in the map and it is not equal to any
                # other two elements and also check if
                # this triplet is not counted already
                # using their indexes
                if li[j]!= 0 and product % (li[j]*li[i]) == 0:
                    if product // (li[j]*li[i]) in li:

                        n = li.index(product//(li[j]*li[i]))

                        if n > i and n > j:
                            flag = 1
                            count+=1
    print(count)

# Driver code
li = [  1, 4, 6, 2, 3, 8 ]
product = 24

# Function call
countTriplets(li,product)

C#

// C# implementation of the above
// approach
using System;
using System.Collections.Generic;
class GFG{

// Method to count such triplets
static int countTriplets(int[] arr,
                         int n, int m)
{
  // Store all the elements
  // in a set
  Dictionary<int,
             int> occ = new Dictionary<int,
                                       int>(n);

  for (int i = 0; i < n; i++)
    occ.Add(arr[i], i);

  int count = 0;

  // Consider all pairs and
  // check for a third number
  // so their product is equal to m
  for (int i = 0; i < n - 1; i++)
  {
    for (int j = i + 1; j < n; j++)
    {
      // Check if current pair divides
      // m or not If yes, then search
      // for (m / arr[i]*arr[j])
      if ((arr[i] * arr[j] <= m) &&
          (arr[i] * arr[j] != 0) &&
          (m % (arr[i] * arr[j]) == 0))
      {
        int check = m / (arr[i] * arr[j]);

        //occ.containsKey(check);
        // Check if the third number
        // is present in the map and
        // it is not equal to any
        // other two elements and also
        // check if this triplet is not
        // counted already using their indexes
        if (check != arr[i] &&
            check != arr[j] &&
            occ.ContainsKey(check) &&
            occ[check] > i &&
            occ[check] > j)
          count++;
      }
    }
  }

  // Return number of triplets
  return count;
}

// Driver code
static void Main()
{
  int[] arr = {1, 4, 6,
               2, 3, 8};
  int m = 24;
  Console.WriteLine(countTriplets(arr,
                                  arr.Length, m));
}
}

// This code is contributed by divyeshrabadiya07

Javascript

<script>

// Javascript program to count triplets with given
// product m

// Function to count such triplets
function countTriplets(arr, n, m)
{

    // Store all the elements in a set
    var occ = new Map();
    for (var i = 0; i < n; i++)
    {
        occ.set(arr[i], i)
    }

    var count = 0;

    // Consider all pairs and check for a
    // third number so their product is equal to m
    for (var i = 0; i < n - 1; i++)
    {
        for (var j = i + 1; j < n; j++)
        {

            // Check if current pair divides m or not
            // If yes, then search for (m / arr[i]*arr[j])
            if ((arr[i] * arr[j] <= m) && (arr[i] * arr[j] != 0) && (m % (arr[i] * arr[j]) == 0)) {
                var check = parseInt(m / (arr[i] * arr[j]));

                var ff = occ.has(check);
                var ans;
                if(ff)
                    ans = occ.get(check)

                // Check if the third number is present
                // in the map and it is not equal to any
                // other two elements and also check if
                // this triplet is not counted already
                // using their indexes
                if (check != arr[i] && check != arr[j]
                    && ff && ans > i
                    && ans > j)
                    count++;
            }
        }
    }

    // Return number of triplets
    return count;
}

// Drivers code
var arr = [1, 4, 6, 2, 3, 8];
var n = arr.length;
var m = 24;
document.write( countTriplets(arr, n, m));

// This code is contributed by importantly.
</script>

Output

3

Time Complexity : O(n²) 
Auxiliary Space : O(n)

New Approach:- Another approach to solve this problem is to sort the array and then use two pointers to find the triplets whose product is equal to the given number. 

Steps:- 

1. Define a function named countTriplets that takes an integer array, the size of the array, and an integer m as arguments.
2. Sort the input array in ascending order using the built-in sort() function of C++.
3. Initialize a variable named count to 0.
4. For each element i in the array from index 0 to n-3:
   *Set two pointers, left and right, to the next and last index of the remaining elements, respectively.
   *While the left pointer is less than the right pointer:
        *If the product of the element i, the element at the left pointer, and the element at the right pointer is equal to m, then increment the count and move the left pointer to the right and the right pointer to the left.
        *Else, if the product is less than m, then move the left pointer to the right.
        *Else, if the product is greater than m, then move the right pointer to the left.
5. Return the value of count.
6. Define the main function.
7. Declare an integer array named arr and initialize it with some values.
8. Calculate the size of the array and store it in an integer variable named n.
9. Define an integer variable named m and initialize it with a value of 24.
10. Call the countTriplets function with the arguments arr, n, and m and print the returned value.

Here’s the implementation:

C++

// C++ program to count triplets with given
// product m
#include <bits/stdc++.h>
using namespace std;

// Function to count such triplets
int countTriplets(int arr[], int n, int m)
{
    sort(arr, arr + n); // Sort the array
    int count = 0;

    // Fix one number and use two pointers to find
    // the other two numbers whose product is equal to m
    for (int i = 0; i < n - 2; i++) {
        int left = i + 1, right = n - 1;
        while (left < right) {
            if (arr[i] * arr[left] * arr[right] == m) {
                count++;
                left++;
                right--;
            }
            else if (arr[i] * arr[left] * arr[right] < m)
                left++;
            else
                right--;
        }
    }

    // Return number of triplets
    return count;
}

// Drivers code
int main()
{
    int arr[] = { 1, 4, 6, 2, 3, 8 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int m = 24;
    cout << countTriplets(arr, n, m);

    return 0;
}

Java

import java.util.Arrays;

public class CountTriplets {
    // Function to count such triplets
    public static int countTriplets(int arr[], int n, int m) {
        Arrays.sort(arr); // Sort the array
        int count = 0;

        // Fix one number and use two pointers to find
        // the other two numbers whose product is equal to m
        for (int i = 0; i < n - 2; i++) {
            int left = i + 1, right = n - 1;
            while (left < right) {
                if (arr[i] * arr[left] * arr[right] == m) {
                    count++;
                    left++;
                    right--;
                } else if (arr[i] * arr[left] * arr[right] < m)
                    left++;
                else
                    right--;
            }
        }

        // Return number of triplets
        return count;
    }

    // Drivers code
    public static void main(String[] args) {
        int arr[] = { 1, 4, 6, 2, 3, 8 };
        int n = arr.length;
        int m = 24;
        System.out.println(countTriplets(arr, n, m));
    }
}

Python3

def countTriplets(arr, n, m):
    arr.sort()  # Sort the array
    count = 0

    # Fix one number and use two pointers to find
    # the other two numbers whose product is equal to m
    for i in range(n - 2):
        left = i + 1
        right = n - 1
        while left < right:
            if arr[i] * arr[left] * arr[right] == m:
                count += 1
                left += 1
                right -= 1
            elif arr[i] * arr[left] * arr[right] < m:
                left += 1
            else:
                right -= 1

    # Return number of triplets
    return count

# Drivers code
arr = [1, 4, 6, 2, 3, 8]
n = len(arr)
m = 24
print(countTriplets(arr, n, m))

C#

using System;

public class Program
{
    // Function to count such triplets
    static int CountTriplets(int[] arr, int n, int m)
    {
        Array.Sort(arr); // Sort the array
        int count = 0;

        // Fix one number and use two pointers to find
        // the other two numbers whose product is equal to m
        for (int i = 0; i < n - 2; i++)
        {
            int left = i + 1, right = n - 1;
            while (left < right)
            {
                if (arr[i] * arr[left] * arr[right] == m)
                {
                    count++;
                    left++;
                    right--;
                }
                else if (arr[i] * arr[left] * arr[right] < m)
                    left++;
                else
                    right--;
            }
        }

        // Return number of triplets
        return count;
    }

    // Drivers code
    static void Main()
    {
        int[] arr = { 1, 4, 6, 2, 3, 8 };
        int n = arr.Length;
        int m = 24;
        Console.WriteLine(CountTriplets(arr, n, m));
    }
}

Javascript

// Function to count such triplets
function countTriplets(arr, n, m) {
  arr.sort((a, b) => a - b); // Sort the array
  let count = 0;

  // Fix one number and use two pointers to find
  // the other two numbers whose product is equal to m
  for (let i = 0; i < n - 2; i++) {
    let left = i + 1, right = n - 1;
    while (left < right) {
      if (arr[i] * arr[left] * arr[right] === m) {
        count++;
        left++;
        right--;
      } else if (arr[i] * arr[left] * arr[right] < m)
        left++;
      else
        right--;
    }
  }

  // Return number of triplets
  return count;
}

// Driver code
const arr = [1, 4, 6, 2, 3, 8];
const n = arr.length;
const m = 24;
console.log(countTriplets(arr, n, m));

Output

3

Time Complexity:- The time complexity of this approach is O(n^2), which is better than the naive approach but worse than the hashing approach. However, this approach has the advantage of not requiring any extra space for storing the elements.

Auxiliary Space:- The auxiliary space of this code is O(1) because the space used is constant and does not depend on the size of the input array or the value of m. The only additional space used is for the variables i, left, right, and count, which require a constant amount of space regardless of the input. The sorting is done in-place, so it does not require any additional space. Therefore, the space complexity of this code is O(1).

This article is contributed by Sahil Chhabra. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.